In a sauté pan cook the chorizo over medium-high heat while breaking up into chunks with a spatula until crisp and fully cooked (about 6 minutes). Add the onions and cook until translucent, about 4 minutes. Transfer to a plated lined with a paper towel to drain any excess grease.
In a saucepan add the wine and lemon juice. Bring slowly to a boil and sauce the heat to medium-low. Add the cheese and cornstarch and whisk until the cheese is fully melted.
Arrange the tortilla chips on a serving platter. Drizzle with the melted cheese mixture. Top with the chorizo mixture. Garnish with cilantro and chives.